When choosing among presidential candidates, Americans find plenty to debate about their fitness for office, experience, and economic and foreign policies. But the framers of the Constitution made no mention of such qualifications; they were primarily concerned that the president be truly American. And one of the ways that a president counted as truly American was to be, in the Constitution’s phrase, a “natural-born citizen.”

In the modern era, this phrase has been particularly contentious. There was the clamor over whether …